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Fibonacci Sequence
★★☆☆☆Middle School
📖Definition
The Fibonacci sequence is where each term is the sum of the two preceding terms. F(1)=1, F(2)=1, F(n)=F(n-1)+F(n-2).
📐Formulas
Fₙ = F_n-1 + F_n-2
Fibonacci recurrence
Fₙ = (φⁿ - ψⁿ)/(√5)
Binet's formula (φ = golden ratio)
lim_n → ∈fty \fracF_n+1Fₙ = φ = \frac1+√52
Convergence to golden ratio
✏️Examples
예제 1
List the first 10 Fibonacci numbers.
📜History
Discovered by: Leonardo Fibonacci (1202)
Fibonacci introduced this sequence while explaining rabbit breeding.
⚡Applications
Nature
Sunflower seeds, shell spirals
Finance
Fibonacci retracement
Algorithms
Fibonacci heap, DP example
🔗Related Documents
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